Step |
Hyp |
Ref |
Expression |
1 |
|
psgnfzto1st.d |
|
2 |
|
ovex |
|
3 |
|
ovex |
|
4 |
|
vex |
|
5 |
3 4
|
ifex |
|
6 |
2 5
|
ifex |
|
7 |
|
eqid |
|
8 |
6 7
|
fnmpti |
|
9 |
8
|
a1i |
|
10 |
|
eqid |
|
11 |
1 10
|
pmtrto1cl |
|
12 |
|
eqid |
|
13 |
10 12
|
pmtrff1o |
|
14 |
|
f1ofn |
|
15 |
11 13 14
|
3syl |
|
16 |
|
simpr |
|
17 |
16
|
iftrued |
|
18 |
|
simpl |
|
19 |
18
|
nnred |
|
20 |
|
fz1ssnn |
|
21 |
1
|
eleq2i |
|
22 |
21
|
biimpi |
|
23 |
22
|
adantl |
|
24 |
20 23
|
sselid |
|
25 |
24
|
nnred |
|
26 |
|
elfz1b |
|
27 |
26
|
simp2bi |
|
28 |
22 27
|
syl |
|
29 |
28
|
adantl |
|
30 |
29
|
nnred |
|
31 |
19
|
lep1d |
|
32 |
|
elfzle2 |
|
33 |
23 32
|
syl |
|
34 |
19 25 30 31 33
|
letrd |
|
35 |
29
|
nnzd |
|
36 |
|
fznn |
|
37 |
35 36
|
syl |
|
38 |
18 34 37
|
mpbir2and |
|
39 |
38 1
|
eleqtrrdi |
|
40 |
39
|
ad2antrr |
|
41 |
17 40
|
eqeltrd |
|
42 |
|
simpr |
|
43 |
42
|
iffalsed |
|
44 |
|
simpr |
|
45 |
44
|
iftrued |
|
46 |
42
|
adantr |
|
47 |
1 20
|
eqsstri |
|
48 |
|
simpllr |
|
49 |
47 48
|
sselid |
|
50 |
|
nn1m1nn |
|
51 |
49 50
|
syl |
|
52 |
51
|
ord |
|
53 |
46 52
|
mpd |
|
54 |
53
|
nnred |
|
55 |
49
|
nnred |
|
56 |
30
|
ad3antrrr |
|
57 |
55
|
lem1d |
|
58 |
48 1
|
eleqtrdi |
|
59 |
|
elfzle2 |
|
60 |
58 59
|
syl |
|
61 |
54 55 56 57 60
|
letrd |
|
62 |
53 61
|
jca |
|
63 |
|
fznn |
|
64 |
35 63
|
syl |
|
65 |
64
|
ad3antrrr |
|
66 |
62 65
|
mpbird |
|
67 |
66 1
|
eleqtrrdi |
|
68 |
45 67
|
eqeltrd |
|
69 |
|
simpr |
|
70 |
69
|
iffalsed |
|
71 |
|
simpllr |
|
72 |
70 71
|
eqeltrd |
|
73 |
68 72
|
pm2.61dan |
|
74 |
43 73
|
eqeltrd |
|
75 |
41 74
|
pm2.61dan |
|
76 |
75
|
ralrimiva |
|
77 |
|
eqid |
|
78 |
77
|
fnmpt |
|
79 |
76 78
|
syl |
|
80 |
77
|
rnmptss |
|
81 |
76 80
|
syl |
|
82 |
|
fnco |
|
83 |
15 79 81 82
|
syl3anc |
|
84 |
|
simpr |
|
85 |
84
|
iftrued |
|
86 |
85
|
fveq2d |
|
87 |
|
fzfi |
|
88 |
1 87
|
eqeltri |
|
89 |
88
|
a1i |
|
90 |
23 21
|
sylibr |
|
91 |
19
|
ltp1d |
|
92 |
19 91
|
ltned |
|
93 |
10
|
pmtrprfv |
|
94 |
89 39 90 92 93
|
syl13anc |
|
95 |
94
|
ad2antrr |
|
96 |
86 95
|
eqtr2d |
|
97 |
88
|
a1i |
|
98 |
39
|
ad4antr |
|
99 |
90
|
ad4antr |
|
100 |
92
|
ad4antr |
|
101 |
10
|
pmtrprfv2 |
|
102 |
97 98 99 100 101
|
syl13anc |
|
103 |
91
|
ad4antr |
|
104 |
|
simpr |
|
105 |
103 104
|
breqtrrd |
|
106 |
19
|
ad4antr |
|
107 |
|
simpr |
|
108 |
47 107
|
sselid |
|
109 |
108
|
nnred |
|
110 |
109
|
ad3antrrr |
|
111 |
106 110
|
ltnled |
|
112 |
105 111
|
mpbid |
|
113 |
112
|
iffalsed |
|
114 |
113 104
|
eqtrd |
|
115 |
114
|
fveq2d |
|
116 |
104
|
oveq1d |
|
117 |
106
|
recnd |
|
118 |
|
1cnd |
|
119 |
117 118
|
pncand |
|
120 |
116 119
|
eqtrd |
|
121 |
102 115 120
|
3eqtr4rd |
|
122 |
|
simplr |
|
123 |
|
simpr |
|
124 |
123
|
necomd |
|
125 |
109
|
ad3antrrr |
|
126 |
25
|
ad4antr |
|
127 |
125 126
|
ltlend |
|
128 |
122 124 127
|
mpbir2and |
|
129 |
108
|
ad3antrrr |
|
130 |
|
simpll |
|
131 |
130
|
ad3antrrr |
|
132 |
|
nnleltp1 |
|
133 |
129 131 132
|
syl2anc |
|
134 |
128 133
|
mpbird |
|
135 |
134
|
iftrued |
|
136 |
135
|
fveq2d |
|
137 |
88
|
a1i |
|
138 |
39
|
ad4antr |
|
139 |
|
simp-5r |
|
140 |
|
simpr |
|
141 |
140
|
ad2antrr |
|
142 |
|
elnn1uz2 |
|
143 |
129 142
|
sylib |
|
144 |
143
|
ord |
|
145 |
141 144
|
mpd |
|
146 |
|
uz2m1nn |
|
147 |
145 146
|
syl |
|
148 |
139 28
|
syl |
|
149 |
147
|
nnred |
|
150 |
131 139 30
|
syl2anc |
|
151 |
125
|
lem1d |
|
152 |
107
|
ad3antrrr |
|
153 |
152 1
|
eleqtrdi |
|
154 |
|
elfzle2 |
|
155 |
153 154
|
syl |
|
156 |
149 125 150 151 155
|
letrd |
|
157 |
147 148 156
|
3jca |
|
158 |
|
elfz1b |
|
159 |
157 158
|
sylibr |
|
160 |
159 1
|
eleqtrrdi |
|
161 |
138 139 160
|
3jca |
|
162 |
131 139 92
|
syl2anc |
|
163 |
|
simpr |
|
164 |
163
|
oveq1d |
|
165 |
109
|
recnd |
|
166 |
165
|
ad3antrrr |
|
167 |
|
1cnd |
|
168 |
166 167
|
npcand |
|
169 |
164 168
|
eqtr2d |
|
170 |
169
|
ex |
|
171 |
170
|
necon3d |
|
172 |
171
|
imp |
|
173 |
149 125 126 151 128
|
lelttrd |
|
174 |
149 173
|
ltned |
|
175 |
174
|
necomd |
|
176 |
162 172 175
|
3jca |
|
177 |
10
|
pmtrprfv3 |
|
178 |
137 161 176 177
|
syl3anc |
|
179 |
136 178
|
eqtr2d |
|
180 |
121 179
|
pm2.61dane |
|
181 |
109
|
ad2antrr |
|
182 |
19
|
ad3antrrr |
|
183 |
25
|
ad3antrrr |
|
184 |
|
simpr |
|
185 |
31
|
ad3antrrr |
|
186 |
181 182 183 184 185
|
letrd |
|
187 |
186
|
ex |
|
188 |
187
|
con3d |
|
189 |
188
|
imp |
|
190 |
189
|
iffalsed |
|
191 |
190
|
fveq2d |
|
192 |
88
|
a1i |
|
193 |
39
|
ad3antrrr |
|
194 |
90
|
ad3antrrr |
|
195 |
107
|
ad2antrr |
|
196 |
193 194 195
|
3jca |
|
197 |
92
|
ad3antrrr |
|
198 |
19
|
ad3antrrr |
|
199 |
25
|
ad3antrrr |
|
200 |
109
|
ad2antrr |
|
201 |
91
|
ad3antrrr |
|
202 |
|
simpr |
|
203 |
199 200
|
ltnled |
|
204 |
202 203
|
mpbird |
|
205 |
198 199 200 201 204
|
lttrd |
|
206 |
198 205
|
ltned |
|
207 |
199 204
|
ltned |
|
208 |
197 206 207
|
3jca |
|
209 |
10
|
pmtrprfv3 |
|
210 |
192 196 208 209
|
syl3anc |
|
211 |
191 210
|
eqtr2d |
|
212 |
180 211
|
ifeqda |
|
213 |
140
|
iffalsed |
|
214 |
213
|
fveq2d |
|
215 |
212 214
|
eqtr4d |
|
216 |
96 215
|
ifeqda |
|
217 |
|
eqidd |
|
218 |
|
eqeq1 |
|
219 |
|
breq1 |
|
220 |
|
oveq1 |
|
221 |
|
id |
|
222 |
219 220 221
|
ifbieq12d |
|
223 |
218 222
|
ifbieq2d |
|
224 |
223
|
adantl |
|
225 |
|
ovex |
|
226 |
|
vex |
|
227 |
225 226
|
ifcli |
|
228 |
227
|
a1i |
|
229 |
130 228
|
ifexd |
|
230 |
217 224 107 229
|
fvmptd |
|
231 |
230
|
fveq2d |
|
232 |
216 231
|
eqtr4d |
|
233 |
|
breq1 |
|
234 |
233 220 221
|
ifbieq12d |
|
235 |
218 234
|
ifbieq2d |
|
236 |
225 226
|
ifex |
|
237 |
2 236
|
ifex |
|
238 |
235 7 237
|
fvmpt |
|
239 |
238
|
adantl |
|
240 |
|
funmpt |
|
241 |
240
|
a1i |
|
242 |
76
|
adantr |
|
243 |
|
dmmptg |
|
244 |
242 243
|
syl |
|
245 |
107 244
|
eleqtrrd |
|
246 |
|
fvco |
|
247 |
241 245 246
|
syl2anc |
|
248 |
232 239 247
|
3eqtr4d |
|
249 |
9 83 248
|
eqfnfvd |
|